Explain the relationship between bond price and bond yield.

First, answer the second question: The i in the denominator is the YTM (Yield to Maturity), meaning that if you purchase the bond at price PV (where PV and YTM can be mutually derived given the cash flows) and hold it to maturity, your realized return will equal the YTM. For example, Bond A is issued at a price of 100 with a YTM of 2%. This means that if you buy Bond A at ¥100 upon issuance and hold it until maturity, your return will be 2%. Suppose Bond B, after being issued for some time, trades in the market at a price of 102 with a YTM of 1.75%. This means that if you purchase Bond B at this moment and hold it to maturity, your return will be 1.75%. This should clarify that if you buy a bond at time t and hold it to maturity without selling it earlier, subsequent changes in the bond’s price or YTM do not affect your actual return—the return you earn depends solely on the YTM at the time of your purchase. Now, answer the first question: In the present-value valuation formula, both the numerator (coupon rate) and the denominator (discount rate or yield) can be decomposed into two components. The numerator can be broken down into the market reference rate (MRR) plus a quoted margin, while the denominator can be broken down into the MRR plus a required margin.

Corporate Finance (8) — Interest Rates and Bond Valuation

2. Pure Discount Bonds — Issued at a discount, i.e., at a price below face value, based on a specified discount rate. The information required to value a pure discount bond includes: (1) Time to maturity (T) = Maturity date – Current date (2) Face value (F) (3) Discount rate (r) The present value of a pure discount bond at time 0 is: For example, consider a 15-year zero-coupon bond with a face value of $1,000. If the market interest rate is 12%, the bond’s value is: 3. Bond Valuation Using Spreadsheets To compute bond price and yield, the following specialized spreadsheet functions are used: (1) PRICE(settlement date, maturity date, coupon rate, yield, redemption value, frequency, basis) (2) YIELD(settlement date, maturity date, coupon rate, price, redemption value, frequency, basis) — Settlement date and maturity date must be specified precisely to the day; redemption value and price must be expressed as percentages of face value. Example below: 8.2 Government Bonds (Treasury Securities) and Corporate Bonds 1. Treasury bills (T-bills) are federal government debt instruments. (1) Short-term T-bills are pure discount bonds with maturities under one year. (2) Intermediate-term Treasury notes (T-notes) are coupon-bearing bonds with maturities between 1 and 10 years. (3) Long-term Treasury bonds (T-bonds) are coupon-bearing bonds with maturities exceeding 10 years. 2. Municipal securities are debt obligations issued by state or local governments. They carry varying default risks and are rated similarly to corporate bonds. Interest income from municipal bonds is exempt from federal income tax. — After-tax yield: Suppose a taxable corporate bond yields 8%, while a municipal bond yields 6%. If your marginal tax rate is 40%, which bond would you choose? 8% × (1 − 0.4) = 4.8% The after-tax yield on the corporate bond is 4.8%, whereas the municipal bond yields 6%; thus, the municipal bond is preferable. At what tax rate would you be indifferent between the two bonds? 8% × (1 − T) = 6% → T = 25% 3. Corporate bonds — Compared with government bonds, corporate bonds carry higher default risk. Due to this added risk, corporate bonds typically promise investors a higher expected return (YTM). (1) Bond ratings – Investment grade: • Highest grade: Moody’s Aaa and S&P’s AAA — exceptional capacity to meet financial commitments. • High grade: Moody’s Aa and S&P’s AA — strong capacity to meet financial commitments. • Medium grade: Moody’s A and S&P’s A — strong capacity, though somewhat more susceptible to adverse economic conditions. • Lower medium grade: Moody’s Baa and S&P’s BBB — adequate capacity, but adverse changes in circumstances could impair ability to meet financial commitments. • Speculative grade: Moody’s Ba and B, and S&P’s BB and B — considered speculative with respect to capacity to pay. • Lowest grade: Moody’s C and S&P’s C and D — highly uncertain ability to repay; in most cases, principal and/or interest payments are already in arrears, signaling default.